Solution 4.4:1f - Revision history

Tek at 13:41, 10 October 2008

2008-10-10T13:41:54Z

←Older revision		Revision as of 13:41, 10 October 2008
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-	We can translate the equation	+	We can translate the equation <math>\sin v=-1/2</math> to the problem of finding those angles in the unit circle which have a ''y''-coordinate of <math>-1/2</math>. If we compare this with the problem that we had in exercise a, where we looked for angles which satisfied <math>\sin v = +1/2</math>, then the situation is the same, except that the angles now lie under, rather than above, the ''x''-axis, due to reflectional symmetry.
-	<math>\sin v=-~~\frac{~~1}{2}</math>	+
-	to the problem of finding those angles in the unit circle which have a y-coordinate of	+
-	<math>-~~\frac{~~1}{2}</math>. If we compare this with the problem that we had in exercise a, where we looked for angles which satisfied	+
-	<math>\sin v=+~~\frac{~~1}{2}</math>, then the situation is the same, except that the angles now lie under, rather than above, the	+
-	~~<math>~~x~~</math>~~	+
-	-axis, due to reflectional symmetry.	+

		+	{\| align="center"
		+	\| align="center" \|[[Image:4_4_1_f-1.gif\|center]]
		+	\| width="20px" \|
		+	\| align="center" \|[[Image:4_4_1_f-2.gif\|center]]
		+	\|-
		+	\| align="center" \|<small>Angle 2π - π/6 = 11π/6</small>
		+	\|\|
		+	\| align="center" \|<small>Angle π + π/6 = 7π/6</small>
		+	\|}

-	~~[[Image:4_4_1_f.gif\|center]]~~	+	The two angles which satisfy <math>\sin v=-1/2</math> lie in the third and fourth quadrants and are <math>v=2\pi - \pi/6 = 11\pi/6</math> and <math>v = \pi + \pi/6 = 7\pi/6</math>.
-		+
-	~~Angle~~	+
-	~~<math>2\pi -\frac{\pi }{6}=\frac{11\pi }{6}</math>~~	+
-	~~Angle~~	+
-	~~<math>\pi +\frac{\pi }{6}=\frac{7\pi }{6}</math>~~	+
-		+
-		+
-	The two angles which satisfy	+
-	<math>\sin v=-~~\frac{~~1}{2}</math>	+
-	lie in the third and fourth quadrants and are	+
-	<math>v=2\pi -~~\frac{~~\pi }{6}=~~\frac{~~11\pi }{6}</math>	+
-	and	+
-	<math>v=\pi +~~\frac{~~\pi }{6}=~~\frac{~~7\pi }{6}</math>	+

Ian at 12:47, 30 September 2008

2008-09-30T12:47:19Z

←Older revision		Revision as of 12:47, 30 September 2008
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-	{{~~NAVCONTENT_START}~~}	+	We can translate the equation
-	<~~center~~> ~~[[Image:4_4_1f.gif]]~~ </~~center~~>	+	<math>\sin v=-\frac{1}{2}</math>
-	{{~~NAVCONTENT_STOP}~~}	+	to the problem of finding those angles in the unit circle which have a y-coordinate of
-		+	<math>-\frac{1}{2}</math>. If we compare this with the problem that we had in exercise a, where we looked for angles which satisfied
		+	<math>\sin v=+\frac{1}{2}</math>, then the situation is the same, except that the angles now lie under, rather than above, the
		+	<math>x</math>
		+	-axis, due to reflectional symmetry.


	[[Image:4_4_1_f.gif\|center]]		[[Image:4_4_1_f.gif\|center]]
		+
		+	Angle
		+	<math>2\pi -\frac{\pi }{6}=\frac{11\pi }{6}</math>
		+	Angle
		+	<math>\pi +\frac{\pi }{6}=\frac{7\pi }{6}</math>
		+
		+
		+	The two angles which satisfy
		+	<math>\sin v=-\frac{1}{2}</math>
		+	lie in the third and fourth quadrants and are
		+	<math>v=2\pi -\frac{\pi }{6}=\frac{11\pi }{6}</math>
		+	and
		+	<math>v=\pi +\frac{\pi }{6}=\frac{7\pi }{6}</math>

Tekbot: Lösning 4.4:1f moved to Solution 4.4:1f: Robot: moved page

2008-09-09T10:01:23Z

Lösning 4.4:1f moved to Solution 4.4:1f: Robot: moved page

←Older revision

Revision as of 10:01, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T07:17:49Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

←Older revision		Revision as of 07:17, 21 August 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[~~Bild~~:4_4_1f.gif]] </center>	+	<center> [[Image:4_4_1f.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}



-	[[~~Bild~~:4_4_1_f.gif\|center]]	+	[[Image:4_4_1_f.gif\|center]]

Madde at 10:35, 19 August 2008

2008-08-19T10:35:49Z

←Older revision		Revision as of 10:35, 19 August 2008
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-	[[Bild:4_4_1_f.gif\|center~~\| Bildtext??~~]]	+	[[Bild:4_4_1_f.gif\|center]]

Madde at 10:33, 19 August 2008

2008-08-19T10:33:00Z

←Older revision		Revision as of 10:33, 19 August 2008
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	<center> [[Bild:4_4_1f.gif]] </center>		<center> [[Bild:4_4_1f.gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}
		+
		+
		+
		+	[[Bild:4_4_1_f.gif\|center\| Bildtext??]]

Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_4_1f.gif {{NAVCONTENT_STOP}}

2008-04-03T12:22:11Z

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_4_1f.gif </center> {{NAVCONTENT_STOP}}

New page

{{NAVCONTENT_START}}
<center> [[Bild:4_4_1f.gif]] </center>
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